Ship hull ice force calculation method for simulation of ship maneuvering motion in level ice area

Abstract

The application discloses a ship ice force calculation method for ship maneuvering motion simulation in a layer ice area, and relates to the field of ship maneuvering motion simulation.The method comprises the following steps: dividing an ice field into a plurality of ice units and determining ice unit position information of each ice unit at a current time; determining each contact ice unit in contact with a ship waterline according to the ice unit position information and the ship waterline position information; determining the contact length of any contact ice unit with the ship waterline and the ship-ice contact speed in combination with ship navigation state parameters; calculating the local force of the contact ice unit on the ship by using an extreme value static ice force formula with a velocity correction term; and superimposing the local forces of each contact ice unit on the ship to obtain the ship ice force at the current time.The application can realize accurate calculation of the ship ice force during simulation of special maneuvering operations such as ship reversing and large-drift-angle maneuvering in a layer ice area, and effectively improves the accuracy and reliability of the ship maneuvering motion simulation in the layer ice area.

Description

Technical Field

[0001] This application relates to the field of ship maneuvering simulation, and in particular to a method for calculating hull ice forces in simulating ship maneuvering in ice-covered areas. Background Technology

[0002] As countries around the world place increasing emphasis on polar regions, ice-coasting vessels, as essential equipment for polar scientific research and development, have received widespread attention. The navigation and maneuverability of vessels in polar ice environments are crucial factors to consider in the design and manufacture of such vessels.

[0003] To evaluate and optimize a ship's ice-covered navigation and maneuvering performance, simulation analysis of the ship's maneuvering motion in layered ice is necessary during the ship's design and development process. Accurately obtaining the hull's ice force load input is crucial when simulating the ship's maneuvering and navigation in layered ice, directly determining the accuracy and reliability of the simulation results.

[0004] Current methods for rapidly obtaining ship hull ice forces primarily rely on direct calculations using analytical, semi-analytical, or empirical ice force formulas. However, existing analytical, semi-analytical, and empirical ice force formulas are all established for the ship's bow navigation state and mostly only focus on longitudinal ice forces. The ice forces calculated using these methods fail to reflect the actual ice forces experienced by the ship during maneuvering, severely impacting the accuracy of simulation results for ship maneuvering in ice-covered areas. Summary of the Invention

[0005] This application addresses the aforementioned problems and technical needs by proposing a method for calculating hull ice forces in the simulation of ship maneuvering motion in layered ice zones. The technical solution of this application is as follows: A method for calculating hull ice forces in a simulation of ship maneuvering motion in layered ice zones includes the following steps: The ice floe region is divided into multiple ice units, and the position information of each ice unit at the current moment is determined. Based on the current position information of each ice element and the position information of the ship's waterline, determine the contact ice elements that are in contact with the ship's waterline at the current moment. Determine the contact length between any contact ice element k and the waterline of the hull by combining ship navigation state parameters. And the ship-ice contact speed, which includes the ship-ice contact speed caused by the ship's bow turning motion, ship's pitching motion, and ship's swaying motion. Using the extreme static ice force formula with a velocity correction term and based on the contact length between the contact ice element k and the waterline of the hull. Calculate the local force exerted on the hull by the contact ice element k at the contact velocity between the ship and the ice. The ice force on the ship at the current moment is obtained by superimposing the local forces exerted on the ship by each contacting ice unit.

[0006] A further technical solution involves determining, based on the current position information of each ice element and the waterline position information of the ship, the contacting ice elements currently in contact with the waterline, including: The outer bounding box of the hull waterline is constructed based on the current waterline position information. The ice units that intersect with the outer bounding box are extracted by combining the ice unit position information of each ice unit at the current time, thus obtaining the neighboring ice units of the hull waterline. The projection of the ship's waterline and all adjacent ice units around the ship's center of gravity onto the waterline plane at the current moment. G Rotate until the bow points to the positive direction of the OX axis of the fixed coordinate system; the positive direction of the OX axis of the fixed coordinate system points to the bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction at the initial moment. An inner rectangular bounding box is constructed based on the rotated waterline position information of the ship. The neighboring ice units that intersect with the inner rectangular bounding box are extracted by combining the ice unit position information of each neighboring ice unit after rotation, so as to obtain each ship perimeter ice unit at the current time. The ship perimeter ice units that are in contact with the waterline of the ship are taken as contact ice units. The inner rectangular bounding box is located inside the outer bounding box. The side length direction of the inner rectangular bounding box is the same as the coordinate axis direction of the fixed coordinate system, and the distance between any side of the inner rectangular bounding box and the rotated waterline of the ship is not less than the longest side length of the ice unit.

[0007] A further technical solution is that the outer bounding box is rectangular in shape and the side length direction of the outer bounding box is the same as the coordinate axis direction of the fixed coordinate system. The neighborhood ice unit for determining the waterline of the ship includes: Based on the position information of the first ice unit obtained from the division and the positions of each corner point of the outer bounding box, determine the row and column indices of the ice units that intersect with each edge of the outer bounding box. Based on the row and column indices of the ice units, the ice units that intersect with the outer bounding box are directly extracted from all the divided ice units, and the ice units that intersect with the outer bounding box are taken as the neighboring ice units of the hull waterline.

[0008] A further technical solution involves determining the local forces, including normal compressive force and tangential frictional force, and identifying the normal compressive force of the contact ice unit k on the hull. and tangential friction include: Determine the ice contact line between ice contact unit k and the ship's waterline; The component of the ship-ice contact velocity in the normal direction of the ship-ice contact line is determined based on the ship-ice contact line and ship navigation parameters. And the component of the ship-ice contact velocity along the tangential direction of the ship-ice contact line. ; The positive direction is along the normal to the ice contact line at the midpoint c and points outward from the waterline of the hull. The positive direction is along the tangent of the ship-ice contact line at the midpoint c and points counterclockwise towards the waterline of the ship. when At that time, determine the normal compressive force exerted on the hull by the contact ice element k at the midpoint c of the ship-ice contact line. ;when At that time, determine the normal compressive force exerted on the hull by the contact ice element k at the midpoint c of the ship-ice contact line. ; when and At that time, determine the tangential friction force of the contact ice element k on the hull at the midpoint c of the ship-ice contact line. Otherwise, determine the tangential friction force exerted by the contact ice element k on the hull at the midpoint c of the ship-ice contact line. ; in, h It's the thickness of the sea ice. It is the effective ice pressure per unit area. and It is the speed correction coefficient. g It is gravitational acceleration. It represents the waterline length of the hull, and sign() is the sign function. It is the coefficient of friction between ship and ice; normal compressive force. The direction of the contact velocity between the ship and the ice is the component of the contact velocity in the normal direction of the contact line between the ship and the ice. Conversely, tangential friction The direction of the component of the ship-ice contact velocity along the tangential direction of the ship-ice contact line. on the contrary.

[0009] A further technical solution involves determining the component of the ship-ice contact velocity between the contact ice unit k and the ship's waterline. and include: Based on the ship's pitch speed in the ship's navigation state parameters Determine the ship-ice contact velocity caused by the ship's swaying motion at point c, the midpoint of the ship-ice contact line. And the velocity direction is along the Gx axis of the motion coordinate system; according to the ship's sway velocity in the ship's navigation state parameters. Determine the ship-ice contact velocity caused by the ship's swaying motion at point c, the midpoint of the ship-ice contact line. And the velocity direction is along the Gy axis of the motion coordinate system; according to the bow roll rate in the ship's navigation state parameters. rThe projection point of the ship's center of gravity onto the waterline. G The location is determined by the position of the ship at the midpoint c of the ship-ice contact line, and the ship-ice contact speed caused by the ship's bow turning motion. And the direction of velocity is perpendicular to the line connecting Gc and points in the direction of the ship's turning. The ship-ice contact velocity at point c, the midpoint of the ship-ice contact line, caused by the ship's swaying motion. Ship-ice contact speed caused by ship swaying motion Speed ​​of contact with ice caused by ship turning Decomposing and transforming the data to the normal and tangential directions of the ship-ice contact line yields:

[0010] in, , , It is the angle between the tangent to the ice contact line at the midpoint c and the OX axis of the fixed coordinate system. It is the angle between the line connecting Gc and the Gx axis of the moving coordinate system. It is the angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system; the positive direction of the Gx axis of the moving coordinate system points to the bow direction at the current moment, and the positive direction of the Gy axis of the moving coordinate system points to the starboard direction at the current moment; the positive direction of the OX axis of the fixed coordinate system points to the bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction at the initial moment.

[0011] A further technical solution involves superimposing the local forces exerted on the hull by each contacting ice unit to obtain the hull ice force at the current moment, including: The normal compressive force exerted on the hull by the contact ice element k at the midpoint c of the ship-ice contact line. and tangential friction The decomposition and transformation yields the components along the Gx axis in the motion coordinate system. Components along the Gy axis :

[0012] in, , It is the angle between the tangent to the line of contact between the ship and the ice at point c and the OX axis of the fixed coordinate system. It is the angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system; the positive direction of the Gx axis of the moving coordinate system points to the bow direction at the current moment, and the positive direction of the Gy axis of the moving coordinate system points to the starboard direction at the current moment; the positive direction of the OX axis of the fixed coordinate system points to the bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction at the initial moment. Calculate the local yaw moment of the contact ice element k with respect to the projection point G of the ship's center of gravity in the waterline. ,in, The bow rocker arm about point G , The bow rocker arm about point G ; The calculated ice forces on the ship at the current moment include longitudinal ice forces. lateral ice force and bow ice-rocking torque , K It is the total number of contact ice units, an integer parameter. K ≥1.

[0013] Its further technical solution is that the method for calculating ship ice force also includes: For any contacting ice unit k, the failure state of the contacting ice unit k is determined based on the ice unit position information and the ship's waterline position information at the current moment. The failure state indicates the degree of damage to the contacting ice unit k after the ship comes into contact with the ice. The contact ice element k is updated based on its failure state, and the process proceeds to the next calculation time.

[0014] A further technical solution is that the failure state includes no failure, partial failure, and complete failure; the position information of any contacting ice unit k includes the position information of each corner point of the contacting ice unit k and the position information of the initial centroid of the contacting ice unit k, wherein the initial centroid is the centroid of the contacting ice unit k at the initial moment; updating the contacting ice unit k according to the failure state of the contacting ice unit k includes: When at most one corner point among all the corner points of the ice contact unit k is located inside the waterline of the hull, the failure state is determined to be non-failure, and the ice contact unit k remains unchanged. When a preset number M corners of all the corners of the contact ice unit k are located inside the waterline of the hull, the failure state is determined to be partial failure, and the shape of the contact ice unit k is changed. When more than a preset number M of the corner points of the contact ice unit k are located inside the waterline of the hull, or when the initial centroid of the contact ice unit k is located inside the waterline of the hull, the failure state is determined to be an overall failure, and the contact ice unit k is removed.

[0015] A further technical solution involves dividing the ice floe area into several ice units, including: The ice floe area is divided into rectangular grids. While keeping the connection relationship between the corner points of the rectangular grid unchanged, the corner points of the rectangular grid are randomly moved within a preset range with their respective positions as the center, forming irregularly shaped ice units.

[0016] A further technical solution is that the ice unit position information of any ship perimeter ice unit m includes the position information of each corner point of the ship perimeter ice unit m; detecting the contact state between any ship perimeter ice unit m and the ship's waterline includes: Based on the position information of each corner point of the ship's perimeter ice unit m and the position information of the ship's waterline at the current moment, it is determined that at the current moment, the ship's perimeter ice unit m has at least one corner point located inside the ship's waterline and at least one corner point located outside the ship's waterline; or, based on the position information of the ship's waterline at the current moment, it is determined that at least one discrete point of the ship's waterline is located inside the ship's perimeter ice unit m, then it is determined that the ship's perimeter ice unit m is in contact with the ship's waterline.

[0017] The beneficial technical effects of this application are: This application proposes a method for calculating hull ice forces in the simulation of ship maneuvering in layered ice zones. By considering the ship-ice contact speed and contact length during navigation in layered ice zones, and utilizing the extreme static ice force formula with a speed correction term, the local forces exerted on the hull by the contacting ice element are calculated. This method can calculate multi-directional hull ice forces on the hull, including longitudinal, lateral, and bow rolling ice moments, effectively solving the problem of unreasonable simulation results caused by traditional methods that only focus on longitudinal ice forces. Furthermore, the method in this application calculates multi-directional hull ice forces based on the ship-ice contact state, enabling accurate calculation of hull ice forces when simulating special maneuvering operations such as star maneuvers, breaking through channels, large drift angle maneuvers, and reversing, effectively improving the accuracy and reliability of ship maneuvering simulation results in layered ice zones.

[0018] By constructing an outer bounding box for the hull waterline and utilizing the row and column indexing of ice elements to directly extract neighboring ice elements, and by rotating the hull waterline and its surrounding neighboring ice elements, and constructing an inner rectangular bounding box for the hull waterline with side lengths aligned with the fixed coordinate system direction, rapid extraction of circumferential ice elements can be achieved through simple logical calculations. This effectively reduces the number of ice elements involved in ship-ice interaction calculations and improves the efficiency of hull ice force calculations.

[0019] Considering the damage to the contact ice unit caused by the ship after contact with ice, the reliability of the ship's ice force calculation results at the next moment is further improved by updating the contact ice unit, thereby ensuring the accuracy of the ship's ice force calculation results throughout the entire maneuvering motion simulation process. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method for calculating ice force on a ship's hull.

[0021] Figure 2 This is a schematic diagram of a fixed coordinate system and a moving coordinate system.

[0022] Figure 3This is a schematic diagram of the waterline of the ship's hull.

[0023] Figure 4 (a) is a schematic diagram of the discrete square grid of ice floes.

[0024] Figure 4 (b) is a schematic diagram of the irregular quadrilateral grid of the ice floes.

[0025] Figure 5 This is a schematic diagram of the random movement of grid corner points.

[0026] Figure 6 (a) is a schematic diagram of the neighboring ice unit of the hull waterline.

[0027] Figure 6 (b) is a schematic diagram of the ice unit around the ship.

[0028] Figure 7 This is a schematic diagram of ship-ice contact.

[0029] Figure 8 This is a schematic diagram of a local coordinate system.

[0030] Figure 9 (a) is the angle between the line connecting Gc and the Gx axis of the moving coordinate system. Schematic diagram.

[0031] Figure 9 (b) is a local coordinate system The angle between the axis and the OX axis of the fixed coordinate system Schematic diagram.

[0032] Figure 10 This is a schematic diagram of the failure state of the contact ice unit.

[0033] Figure 11 This is a schematic diagram of the local forces exerted on the hull by the contact ice unit. Detailed Implementation

[0034] The specific embodiments of this application will be further described below with reference to the accompanying drawings.

[0035] This application proposes a method for calculating hull ice forces in the simulation of ship maneuvering motion in layered ice areas. Please refer to the following: Figure 1 The flowchart shown below illustrates the specific steps: Step 1: Divide the ice floe region into multiple ice units and determine the position information of each ice unit at the current moment.

[0036] To clearly indicate the positions of the ice elements and the waterline in the hull ice force calculation, we first define the coordinate system used in the hull ice force calculation process. Please refer to [reference needed]. Figure 2A fixed coordinate system O-XY is pre-established, directly connected to the earth. Its origin O is any point outside the waterline of the ship. The positive direction of the OX axis is the bow direction of the ship at the initial moment, and the positive direction of the OY axis is the starboard direction of the ship at the initial moment. A moving coordinate system G-xy is pre-established, moving with the ship. Its origin G is the projection point G of the ship's center of gravity onto the waterline. The positive direction of the Gx axis is the bow direction of the ship at the current moment, and the positive direction of the Gy axis is the starboard direction of the ship at the current moment. The angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system is... For heading angle and heading angle The Gx axis is positive in the clockwise direction of the OX axis.

[0037] In a fixed coordinate system, the waterline of the ship's hull is discretized into multiple discrete points, and the position information of the waterline is determined, including the position of each discrete point. Specifically, a finite number of discrete points are taken at certain intervals along the waterline. Where the shape of the waterline changes drastically, the interval between adjacent discrete points should be appropriately reduced. The number of discrete points is determined to accurately represent the geometry of the waterline. The waterline can then be represented by a series of continuous line segments formed by adjacent discrete points. The closed polyline formed by all continuous line segments is as follows: Figure 3 As shown.

[0038] In a fixed coordinate system, the ice floe region is divided into multiple ice units. This application uses a rectangular mesh partitioning method; however, a square mesh can also be used for computational simplicity. Figure 4 As shown in (a). However, in practical applications, whether it is a rectangular grid or a square grid, this type of regular quadrilateral grid arrangement with obvious directional orientation has certain defects in describing the randomness of sea ice destruction and fracturing. Therefore, it is necessary to perform some randomization processing on the grid shape.

[0039] In one embodiment, when dividing the ice floe area into rectangular grids, while preserving the connection relationships between the corner points of the rectangular grids, the corner points of the rectangular grids are randomly moved within a preset range with their respective positions as the center, forming irregularly shaped ice units. Specifically, such as... Figure 4 As shown in (b), the four corner points of each grid are randomly moved within a certain range with their positions as the center to form irregular quadrilateral grid units. Each irregular quadrilateral grid unit is an ice unit that constitutes the whole ice floe.

[0040] The random movement process of each corner point is as follows: Figure 5 As shown, the random movement range of each corner point is defined as within a circle with its current position as the center and radius R. In a fixed coordinate system, if the original position coordinates of any corner point i are... Its position coordinates after random movement for:

[0041]

[0042]

[0043]

[0044] Where rand[1] represents a function for generating random numbers between 0 and 1; for rectangular grids, integer parameters... The non-uniform grid discretization of the ice floe region is completed by randomly moving each corner point of the rectangular grid. It should be noted that when randomly moving the corner points of the rectangular grids obtained from dividing the ice floe region, to improve the efficiency of corner point movement, only the shape of a few rectangular grids can be changed. However, to improve the accuracy of ice force calculation, the shape of all rectangular grids can be changed so that each ice element is an irregular quadrilateral grid. Simultaneously, when moving each rectangular grid corner point, the position offset of the corner points shared by adjacent rectangular grids should be the same. To further improve the efficiency of ice grid corner point movement, if a corner point is shared by more than one rectangular grid, only one random movement is needed. The position coordinates after the random movement are the position coordinates of the corresponding corner points of the other rectangular grids sharing this corner point after random movement.

[0045] The centroid of the irregular quadrilateral ice unit obtained at the initial time is used as the initial centroid of each irregular quadrilateral ice unit, and the position coordinates of the initial centroid of each irregular quadrilateral ice unit are... The calculation formula is as follows:

[0046]

[0047] Step 2: Determine the contact ice units that are in contact with the ship's waterline at the current moment based on the ice unit position information and the ship's waterline position information at the current moment.

[0048] During actual navigation in an ice-covered area, only the ice units in contact with the hull exert direct forces on the ship. Therefore, to reduce unnecessary calculations, it is only necessary to extract the ice units in contact with the hull within the ice-covered area. In one embodiment, the specific method for determining each contacting ice unit currently in contact with the waterline of the hull is as follows: (1) Construct the outer bounding box of the hull waterline based on the current waterline position information, and extract the ice units that intersect with the outer bounding box by combining the ice unit position information of each ice unit at the current time, so as to obtain the ice units in each neighborhood of the hull waterline.

[0049] The outer bounding box is constructed to define a larger area to extract all ice units in contact with the ship's waterline, serving as a preliminary screening tool. The shape of the outer bounding box can be arbitrary; however, for computational simplicity and efficiency, the outer bounding box in this application is rectangular, with its side length aligned with the coordinate axes of the fixed coordinate system. Therefore, the neighborhood ice units within the ship's waterline are determined as follows: Based on the position information of the first ice unit obtained from the division and the positions of each corner point of the outer bounding box, determine the row and column indices of the ice units that intersect with each edge of the outer bounding box.

[0050] Specifically, if the discretized ice floe has I rows and J columns of ice units, and within a fixed coordinate system, the original coordinates of the top-left corner of the first row and first column ice unit are... Meanwhile, the minimum horizontal and vertical coordinates of the four corner points of the outer bounding box of the constructed hull waterline in the fixed coordinate system are: The maximum x and y coordinates are .

[0051] like If the outer bounding box does not intersect with the ice floe, it means there are no ice elements around the ship, and the ice elements cannot interact with the hull, i.e., the ice force on the hull is 0. Conversely, the row and column indices of the ice elements that intersect with each side of the outer bounding box are calculated using the following formula:

[0052]

[0053]

[0054]

[0055] Among them, ceil() represents the floor function (round up to the nearest integer), mod() represents the modulo function, max() represents the maximum value function, and min() represents the minimum value function; This represents the width of the rectangular ice cell before the corner points are randomly moved; This represents the length of a rectangular ice cell before the corner points are randomly moved; for the case of a discrete ice floe region with a square grid. and equal; i , ii , j , jjThis represents the row and column indices of ice cells that intersect with each edge of the outer bounding box, representing the th ice cell in the ice floe. i ~ ii Okay, number j ~ jj The ice units in the column intersect with the outer bounding box.

[0056] Based on the row and column indices of the ice units, ice units that intersect with the outer bounding box are directly extracted from all the divided ice units. These ice units that intersect with the outer bounding box are then considered as neighboring ice units of the ship's waterline. Figure 6 As shown in (a).

[0057] (2) Project the current waterline and each neighboring ice unit around the ship's center of gravity onto the waterline plane. G Rotate until the bow points in the positive direction of the OX axis of the fixed coordinate system.

[0058] In a fixed coordinate system, rotate the neighboring ice elements and the ship's waterline inversely around point G by an angle. This ensures that the bow direction of the ship after the reverse rotation is consistent with its initial bow direction, meaning that the coordinate system of motion after the rotation remains parallel to the coordinate axes of the geodetic coordinate system.

[0059] (3) Construct an inner rectangular bounding box based on the waterline position information of the rotated hull, and extract the neighboring ice units that intersect with the inner rectangular bounding box by combining the ice unit position information of each neighboring ice unit after rotation, so as to obtain each ship perimeter ice unit at the current time, and take the ship perimeter ice unit that is in contact with the waterline of the hull as the contact ice unit.

[0060] The inner rectangular bounding box is located inside the outer bounding box. The side length of the inner rectangular bounding box is aligned with the coordinate axes of the fixed coordinate system, and the distance between any side of the inner rectangular bounding box and the rotated hull waterline is not less than the longest side length of the ice element. For example, in the case of a square grid discrete ice floe region, the distance between the inner rectangular bounding box and the rotated hull waterline is not less than the side length of the square grid. Figure 6 As shown in (b).

[0061] Since the four sides of the inner rectangular bounding box align with the coordinate axes of the fixed coordinate system, the ice elements around the ship can be extracted using simple logical judgment. Specifically, the minimum x and y coordinates of the four corner points of the inner rectangular bounding box are denoted as follows: The maximum x and y coordinates are At this point, traversing each rotated neighboring ice unit, if its initial centroid position passes through the rotated coordinates... If the following logical condition is met, then it is not a perimeter ice unit; otherwise, it is a perimeter ice unit. The logical condition is:

[0062] In one embodiment, the ice element position information of any ship perimeter ice element m includes the position information of each corner point of the ship perimeter ice element m and the position information of its initial centroid. Detecting the contact state between any ship perimeter ice element m and the waterline of the hull includes: Based on the position information of each corner point of the ship's perimeter ice unit m and the position information of the ship's waterline at the current moment, it is determined that at the current moment, the ship's perimeter ice unit m has at least one corner point located inside the ship's waterline and at least one corner point located outside the ship's waterline; or, based on the position information of the ship's waterline at the current moment, it is determined that at least one discrete point of the ship's waterline is located inside the ship's perimeter ice unit m, then it is determined that the ship's perimeter ice unit m is in contact with the ship's waterline.

[0063] For ice elements around a ship that are irregular quadrilaterals, since the waterline is a closed polyline composed of a series of continuous line segments between adjacent discrete points, when all four corner points of ice element m are located inside the waterline, ice element m is not in contact with the waterline. However, for ice elements m located at the fore and aft points of the waterline, when all four corner points are located outside the waterline, but some discrete points on the waterline are located inside ice element m, ice element m is in contact with the waterline. When all corner points of ice element m are located inside the waterline, but the intersection of the waterline and ice element m is between two discrete points, no discrete point is located inside ice element m, but ice element m is still in contact with the waterline. Therefore, the positional relationship between the corner points of ice element m and the waterline, as well as the positional relationship between the discrete points on the waterline and ice element m, should be used simultaneously as criteria for determining the contact state. When only one of the four corner points of the ice element m is located above the waterline of the hull, it indicates that the ice element m is in single-point contact with the waterline of the hull. At this time, the contact length is 0, and the ice element does not exert any force on the hull.

[0064] Step 3: Determine the contact length between any ice contact unit k and the waterline of the hull, based on the ship's navigation state parameters. And the ship-ice contact speed, which includes the ship-ice contact speed caused by the ship's bow turning motion, ship's pitching motion, and ship's swaying motion.

[0065] Using the extreme static ice force formula with a velocity correction term and based on the contact length between the contact ice element k and the waterline of the hull. Calculate the local force exerted on the ship hull by the contact ice element k at the contact speed with the ship.

[0066] Iterate through all extracted ice contact elements and calculate the local force exerted on the hull by any ice contact element k. In one embodiment, the local force includes normal compressive force and tangential frictional force. Determine the normal compressive force of ice contact element k on the hull. and tangential friction The specific steps are as follows: (1) Determine the ice contact line between the ice contact unit k and the waterline of the ship.

[0067] like Figure 7 As shown in the figure, the dashed line represents the waterline of the ship's hull, the irregular quadrilateral is the contact ice element k, points a and b are the intersections of the contact ice element k and the waterline of the ship's hull, respectively, and point c is the midpoint of the line connecting a and b. The coordinates of point a in the fixed coordinate system are... The coordinates of point b in the fixed coordinate system are: The line connecting a and b is the ship-ice contact line, and the length of the ship-ice contact line is the contact length between the ice contact unit k and the waterline of the ship. .

[0068] The ship-ice contact line is the line connecting points a and b. Based on the actual interaction between ice layers and the ship hull, this application uses the straight segment between a and b as the ship-ice contact line. This simplifies the calculation and improves efficiency while ensuring accuracy. Therefore, the contact length can be determined based on the length of the straight segment ab. The specific calculation formula is as follows:

[0069] (2) Determine the component of the ship-ice contact velocity of the contact ice unit k with the ship's waterline in the normal direction of the ship-ice contact line based on the ship-ice contact line and the ship's navigation state parameters. And the component of the ship-ice contact velocity along the tangential direction of the ship-ice contact line. ; The positive direction is along the normal to the ice contact line at the midpoint c and points outward from the waterline of the hull. The positive direction is along the tangent of the ship-ice contact line at the midpoint c and points counterclockwise towards the waterline of the ship.

[0070] The midpoint c of the ship-ice contact line is taken as the point of application of the local force exerted by the contact ice element k on the ship hull. To facilitate the expression of the direction of the local force, a local coordinate system is established in advance. ,like Figure 8 As shown, the origin of the local coordinate system is taken as the midpoint c of the ship-ice contact line. Using the tangent to the ice contact line and pointing counterclockwise towards the waterline as the local coordinate system The local coordinate system is defined by the positive axis, with the normal to the ice contact line pointing outwards from the waterline. Positive direction of the axis. Since line ab is a straight line segment, the tangent to the ship-ice contact line is along line ab, and the normal to the ship-ice contact line is perpendicular to line ab.

[0071] The relationship between the local coordinate system, the fixed coordinate system, and the moving coordinate system is as follows: Figure 9 As shown, the angle between the line connecting Gc and the Gx axis of the moving coordinate system is... ,like Figure 9 As shown in (a), the line connecting Gc is positive in the clockwise direction along the Gx axis; the local coordinate system... The angle between the axis and the OX axis of the fixed coordinate system is ,like Figure 9 As shown in (b), with The axis is positive in the clockwise direction of the OX axis. Because the tangent to the ship-ice contact line at point c intersects with the local coordinate system... Since the axes are aligned, the angle between the tangent at point c on the ship-ice contact line and the OX axis of the fixed coordinate system is also θ. .

[0072] In one embodiment, the component of the ship ice contact velocity between the contact ice unit k and the ship's waterline is determined. and The specific method is as follows: Based on the ship's pitch speed in the ship's navigation state parameters Determine the ship-ice contact velocity caused by the ship's swaying motion at point c, the midpoint of the ship-ice contact line. And the velocity direction is along the Gx direction of the motion coordinate system; according to the ship's sway speed in the ship's navigation state parameters. Determine the ship-ice contact velocity caused by the ship's swaying motion at point c, the midpoint of the ship-ice contact line. And the velocity direction is along the Gy direction of the motion coordinate system; according to the bow roll rate in the ship's navigation state parameters r The projection point of the ship's center of gravity onto the waterline. G The location is determined by the position of the ship at the midpoint c of the ship-ice contact line, and the ship-ice contact speed caused by the ship's bow turning motion. The velocity direction is perpendicular to the line connecting Gc and points towards the direction of the ship's turn; where the ship's pitching speed is... Ship sway speed and bow roll rate r direction such as Figure 7 As shown. If the coordinates of point G in a fixed coordinate system are... Furthermore, the coordinates of point c are , recorded as Then the length of the line connecting Gc .

[0073] The ship-ice contact velocity at point c, the midpoint of the ship-ice contact line, caused by the ship's swaying motion. Ship-ice contact speed caused by ship swaying motion Speed ​​of contact with ice caused by ship turning The specific process of decomposing and converting the data to the normal and tangential directions of the ship-ice contact line is as follows: The ship-ice contact velocity at point c, the midpoint of the ship-ice contact line, caused by the ship's swaying motion. Ship-ice contact speed caused by ship swaying motion Speed ​​of contact with ice caused by ship turning The components of the ship-ice contact velocity in the Gx-axis direction of the moving coordinate system are obtained by decomposing the velocity onto the Gx-axis of the moving coordinate system. And the components of the ship-ice contact velocity in the Gy axis direction of the motion coordinate system are obtained by decomposing it into the Gy axis direction of the motion coordinate system. .

[0074] The component of the ship-ice contact velocity along the Gx-axis of the moving coordinate system. and G Components in the y-axis direction The components of the ship-ice contact velocity in the fixed coordinate system are obtained by decomposing the velocity onto the OX axis. And the components of the ship-ice contact velocity in the OY axis direction of the fixed coordinate system are obtained by decomposing it into the OY axis direction. , It is the angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system.

[0075] The component of the ship-ice contact velocity along the OX axis in a fixed coordinate system. and components in the OY axis direction By decomposing the velocity of the contact ice element k with the waterline at the midpoint c of the contact line, along the normal direction of the contact line, we obtain the component of the ship-ice contact velocity along the normal direction of the contact line. And the component of the ship-ice contact velocity of the contact ice element k with the waterline at the midpoint c of the ship-ice contact line in the tangential direction of the ship-ice contact line. ; It is the angle between the tangent of the ship-ice contact line and the OX axis of the fixed coordinate system.

[0076] (3) It can be based on the component of the ship-ice contact velocity in the normal direction. Calculate the normal compressive force of contact ice element k on the hull. The specific calculation method is as follows: Using the midpoint c of the ship-ice contact line as the normal compressive force The point of application of the force, when At that time, determine the normal compressive force of the contact ice element k on the hull. ;because The direction pointing outwards from the waterline of the hull is considered positive, so when At this time, the ship does not compress the ice unit, but tends to move away from the ice unit, so there is no compressive force between the ship and the ice unit; when At that time, determine the normal compressive force exerted on the hull by the contact ice element k at the midpoint c of the ship-ice contact line. ,in, h It's the thickness of the sea ice. It is the effective ice pressure per unit area; It can be calculated using the extreme static ice force formula. , It is the ice strength coefficient. This is a reference for ice thickness, generally taken as 1 meter; This is an empirical coefficient, which is set to -0.16 in this application; It is also an empirical coefficient, and when h When <1 meter, ,when Rice time, =-0.3.

[0077] Since the contact speed between the ship and ice is closely related to the magnitude of the ice force when a ship is actually navigating in a layered ice zone, a velocity correction term is introduced into the extreme static ice force formula to improve its applicability in calculating the ice force on the ship's hull during navigation in a layered ice zone. This is done considering the influence of the contact speed between the ship and ice and the normal compressive force. The direction points inward normal to the ship-ice contact line. Therefore, based on the extreme static ice force formula with introduced velocity correction, the normal compressive force... The calculation is expressed as follows:

[0078] in, and This is the speed correction factor; its specific value can be set according to the actual application. g It is gravitational acceleration. It is the waterline length of the hull and the normal compressive force. The direction of the contact velocity between the ship and the ice is the component of the contact velocity in the normal direction of the contact line between the ship and the ice. Conversely, along the normal to the ship-ice contact line at the midpoint c and pointing inwards towards the waterline of the hull.

[0079] (4) The normal compressive force of the contact ice unit k on the hull can be determined based on the contact ice unit k. and the component of the ship-ice contact velocity in the tangential direction of the ship-ice contact line. Calculate the tangential friction force of the contact ice element k on the hull. The specific calculation method is as follows: Friction is generated by the relative motion between the hull and the contacting ice element along the tangential direction of the contact line, and its magnitude is proportional to the magnitude of the compressive force exerted by the ice element. Friction only occurs when the tangential relative velocity between the hull and the contacting ice element is not zero, and when a compressive force exists between them. Therefore, when... and At that time, the midpoint c of the ship-ice contact line is taken as the tangential friction force. Determine the point of application of the force, and the tangential frictional force of the contact ice element k on the hull. Otherwise, determine the tangential friction force exerted by the contact ice element k on the hull at the midpoint c of the ship-ice contact line. ; Where sign() is the sign function. Indicates taking symbols, It is the coefficient of friction between the ship and ice, and the tangential friction force. Along the tangent at the midpoint c of the ship-ice contact line and the component of the ship-ice contact velocity in the tangential direction of the ship-ice contact line. The directions are opposite.

[0080] When a ship actually navigates in an ice-covered area, collisions with ice elements can damage them. The degree of damage varies depending on the extent of contact; ice elements with minor damage will continue to exert forces on the ship's hull, while those with significant damage will not. To ensure the accuracy of the simulation results, during the ship navigation simulation, after calculating the local forces of ship-ice interaction at each calculation moment, it is necessary to determine the failure state of the contacting ice element based on its relative position to the waterline and then update the contacting ice element accordingly.

[0081] In one embodiment, for any contacting ice unit k, the failure state of the contacting ice unit k is determined based on the ice unit position information and the ship's waterline position information at the current moment. The failure state indicates the degree of damage to the contacting ice unit k after the ship comes into contact with the ice. The contacting ice unit k is updated based on the failure state of the contacting ice unit k, and the next calculation time is entered.

[0082] Failure states include no failure, partial failure, and complete failure. The position information of any contacting ice element k includes the position information of each corner point of the contacting ice element k and the position information of the initial centroid of the contacting ice element k. The initial centroid is the centroid of the contacting ice element k at the initial moment. Updating the contacting ice element k according to its failure state includes: When at most one corner point among all the corner points of the ice contact unit k is located inside the waterline of the hull, the failure state is determined to be non-failure, and the ice contact unit k remains unchanged.

[0083] When a preset number M corners of all the corners of the contact ice unit k are located inside the waterline of the hull, the failure state is determined to be partial failure. The shape of the contact ice unit k is changed. Specifically, the part of the contact ice unit k located inside the waterline of the hull is deleted, and the part located outside the waterline of the hull is retained and combined with the ship-ice contact line ab to form a new ice unit shape.

[0084] When more than a preset number M of the corner points of the contact ice unit k are located inside the waterline of the hull, or when the initial centroid of the contact ice unit k is located inside the waterline of the hull, the failure state is determined to be an overall failure. The contact ice unit k is then removed so that it falls off the ice floe and no longer participates in the ship-ice interaction calculation, meaning that it no longer exerts ice force on the hull.

[0085] The preset number M is set according to the shape of the contact ice unit. For irregular quadrilateral contact ice units, such as... Figure 10 As shown, if none of the four corner points of the contact ice unit k are located inside the waterline of the hull, or only one corner point is located inside the waterline of the hull, the failure state of the contact ice unit k is not failed; if two corner points are located inside the waterline of the hull, the failure state of the contact ice unit k is partially failed; if three or more corner points are located inside the waterline of the hull, the failure state of the contact ice unit k is completely failed; for the contact ice unit k that contacts the fore and aft tips of the waterline of the hull, if the initial centroid of the contact ice unit k is located inside the waterline of the hull, but there are no corner points or fewer than three corner points located inside the waterline of the hull, the failure state of the contact ice unit k is also completely failed.

[0086] Step 4: Superimpose the local forces exerted on the hull by each contacting ice unit to obtain the hull ice force at the current moment.

[0087] When calculating the overall ice force, the midpoint c of the ship-ice contact line is taken as the point of force application. The normal compressive force and tangential frictional force exerted on the ship by each contacting ice element k are superimposed to obtain the overall ice force exerted by the ice floe on the ship. In one embodiment, the specific process of superimposing the local forces exerted on the ship by each contacting ice element to obtain the current ice force on the ship is as follows: Taking the midpoint c of the ship-ice contact line as the point of force application, the normal compressive force of the contact ice element k on the ship hull is... and tangential friction The components of the material along the OX axis in a fixed coordinate system are obtained through decomposition and transformation. and components on the OY axis :

[0088] The components of the force exerted by the contact ice element k on the hull along the OX axis of a fixed coordinate system. Components along the OY axis The decomposition and transformation yields its components along the Gx axis in the motion coordinate system. and components on the Gy axis :

[0089] Calculate the local yaw moment of the contact ice element k with respect to the projection point G of the ship's center of gravity in the waterline. ,in, The bow rocker arm about point G , The bow rocker arm about point G , Represents the Gc vector. Represents the vector Gx. Represents the Gy vector. This represents the magnitude of the vector Gx. This represents the magnitude of the Gy vector.

[0090] The components of the force exerted on the hull by the contact ice element k obtained from the decomposition along the Gx axis of the moving coordinate system. as well as The component of the yaw arm about point G along the Gy axis in the motion coordinate system. as well as Please refer to the reference for the bow rocker arm at point G. Figure 11 .

[0091] The calculated ice force on the ship at the current moment includes the longitudinal ice force acting on the ship along the longitudinal direction of the hull. Lateral ice force along the hull and bow ice-rocking torque , K It is the total number of contact ice units, an integer parameter. K ≥1.

[0092] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that are directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.

Claims

1. A method for calculating hull ice forces in simulating ship maneuvering motion in layered ice zones, characterized in that, The method for calculating the ice force of the ship's hull includes: The ice floe region is divided into multiple ice units, and the position information of each ice unit at the current moment is determined. Based on the current position information of each ice element and the position information of the ship's waterline, determine the contact ice elements that are in contact with the ship's waterline at the current moment. Determine the contact length between any contact ice element k and the waterline of the hull by combining ship navigation state parameters. And the ship-ice contact speed, which includes the ship-ice contact speed caused by the ship's bow turning motion, ship's pitching motion, and ship's swaying motion. Using the extreme static ice force formula with a velocity correction term and based on the contact length between the contact ice element k and the waterline of the hull. Calculate the local force exerted on the hull by the contact ice element k at the contact velocity between the ship and the ice. The hull ice force at the current moment is obtained by superimposing the local forces exerted on the hull by each contacting ice unit; The local forces include normal compressive force and tangential frictional force. The normal compressive force of the contact ice unit k on the hull is determined. and tangential friction include: Determine the ice contact line between ice contact unit k and the ship's waterline; The component of the ship-ice contact velocity in the normal direction of the ship-ice contact line is determined based on the ship-ice contact line and ship navigation parameters. And the component of the ship-ice contact velocity along the tangential direction of the ship-ice contact line. ; The positive direction is along the normal to the ice contact line at the midpoint c and points outward from the waterline of the hull. The positive direction is along the tangent of the ship-ice contact line at the midpoint c and points counterclockwise towards the waterline of the ship. when At that time, determine the normal compressive force exerted on the hull by the contact ice element k at the midpoint c of the ship-ice contact line. ;when At that time, determine the normal compressive force exerted on the hull by the contact ice element k at the midpoint c of the ship-ice contact line. ; when and At that time, determine the tangential friction force of the contact ice element k on the hull at the midpoint c of the ship-ice contact line. Otherwise, determine the tangential friction force exerted by the contact ice element k on the hull at the midpoint c of the ship-ice contact line. ; in, h It's the thickness of the sea ice. It is the effective ice pressure per unit area. g It is gravitational acceleration. It is the length of the ship's waterline. and These are the velocity correction coefficients, and sign() is the sign function. It is the coefficient of friction between the ship and ice; normal compressive force. The direction of the contact velocity between the ship and the ice is the component of the contact velocity in the normal direction of the contact line between the ship and the ice. Conversely, tangential friction The direction of the component of the ship-ice contact velocity along the tangential direction of the ship-ice contact line. on the contrary; The hull ice forces at the current moment are obtained by superimposing the local forces exerted on the hull by each contacting ice element: The normal compressive force exerted on the hull by the contact ice element k at the midpoint c of the ship-ice contact line. and tangential friction The decomposition and transformation yields the components along the Gx axis in the motion coordinate system. Components along the Gy axis : in, , It is the angle between the tangent to the line of contact between the ship and the ice at point c and the OX axis of the fixed coordinate system. It is the angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system; the positive direction of the Gx axis of the moving coordinate system points to the bow direction at the current moment, and the positive direction of the Gy axis of the moving coordinate system points to the starboard direction at the current moment; the positive direction of the OX axis of the fixed coordinate system points to the bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction at the initial moment. Calculate the local yaw moment of the contact ice element k with respect to the projection point G of the ship's center of gravity in the waterline. ,in, The bow rocker arm about point G , The bow rocker arm about point G ; The calculated ice forces on the ship at the current moment include longitudinal ice forces. lateral ice force and bow ice-rocking torque , K It is the total number of contact ice units, an integer parameter. K ≥1.

2. The method for calculating ship hull ice force according to claim 1, characterized in that, The step of determining the contacting ice units that are in contact with the ship's waterline at the current moment based on the ice unit position information and the ship's waterline position information at the current moment includes: Based on the current waterline position information, an outer bounding box for the waterline is constructed. Then, by combining the current ice unit position information of each ice unit, ice units that intersect with the outer bounding box are extracted to obtain the neighboring ice units of the waterline. The projection of the ship's waterline and all adjacent ice units around the ship's center of gravity onto the waterline plane at the current moment. G Rotate until the bow points to the positive direction of the OX axis of the fixed coordinate system; the positive direction of the OX axis of the fixed coordinate system points to the bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction at the initial moment. An inner rectangular bounding box is constructed based on the rotated hull waterline position information. Then, by combining the position information of each neighboring ice unit after rotation, neighboring ice units that intersect with the inner rectangular bounding box are extracted to obtain the current hull perimeter ice units. The hull perimeter ice units that are in contact with the hull waterline are designated as contact ice units. The inner rectangular bounding box is located inside the outer bounding box. The side length direction of the inner rectangular bounding box is the same as the coordinate axis direction of the fixed coordinate system, and the distance between any side of the inner rectangular bounding box and the rotated hull waterline is not less than the longest side length of the ice unit.

3. The method for calculating ship hull ice force according to claim 2, characterized in that, The outer bounding box is rectangular in shape, and the side length of the outer bounding box is in the same direction as the coordinate axis of the fixed coordinate system. The neighborhood ice unit that determines the waterline of the ship includes: Based on the position information of the first ice unit obtained from the division and the positions of each corner point of the outer bounding box, determine the row and column indices of the ice units that intersect with each edge of the outer bounding box. According to the row and column index of the ice unit, the ice units that intersect with the outer bounding box are directly extracted from all the divided ice units, and the ice units that intersect with the outer bounding box are taken as the neighboring ice units of the hull waterline.

4. The method for calculating ship hull ice force according to claim 1, characterized in that, Determine the components of the ship-ice contact velocity between the contact ice element k and the ship's waterline. and include: Based on the ship's pitch speed in the ship's navigation state parameters Determine the ship-ice contact velocity caused by the ship's swaying motion at point c, the midpoint of the ship-ice contact line. And the velocity direction is along the Gx axis of the motion coordinate system; according to the ship's sway speed in the ship's navigation state parameters. Determine the ship-ice contact velocity caused by the ship's swaying motion at point c, the midpoint of the ship-ice contact line. And the velocity direction is along the Gy axis of the motion coordinate system; according to the bow roll rate in the ship's navigation state parameters. r The projection point of the ship's center of gravity onto the waterline. G The location is determined by the position of the ship at the midpoint c of the ship-ice contact line, and the ship-ice contact speed caused by the ship's bow turning motion. And the direction of velocity is perpendicular to the line connecting Gc and points in the direction of the ship's turning. The ship-ice contact velocity at point c, the midpoint of the ship-ice contact line, caused by the ship's swaying motion. Ship-ice contact speed caused by ship swaying motion Speed ​​of contact with ice caused by ship turning Decomposing and transforming the data to the normal and tangential directions of the ship-ice contact line yields: in, , , It is the angle between the tangent to the ice contact line at the midpoint c and the OX axis of the fixed coordinate system. It is the angle between the line connecting Gc and the Gx axis of the moving coordinate system. It is the angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system; the positive direction of the Gx axis of the moving coordinate system points to the bow direction at the current moment, and the positive direction of the Gy axis of the moving coordinate system points to the starboard direction at the current moment; the positive direction of the OX axis of the fixed coordinate system points to the bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction at the initial moment.

5. The method for calculating ship hull ice force according to claim 1, characterized in that, The method for calculating ship ice force also includes: For any contacting ice unit k, the failure state of the contacting ice unit k is determined based on the ice unit position information and the ship's waterline position information at the current moment. The failure state indicates the degree of damage to the contacting ice unit k after the ship comes into contact with the ice. The contact ice element k is updated based on its failure state, and the process proceeds to the next calculation time.

6. The method for calculating ship hull ice force according to claim 5, characterized in that, The failure states include no failure, partial failure, and complete failure. The position information of any contacting ice unit k includes the position information of each corner point of the contacting ice unit k and the position information of the initial centroid of the contacting ice unit k. The initial centroid is the centroid of the contacting ice unit k at the initial moment. Updating the contacting ice unit k according to its failure state includes: When at most one corner point among all the corner points of the ice contact unit k is located inside the waterline of the hull, the failure state is determined to be non-failure, and the ice contact unit k remains unchanged. When a predetermined number M corners of the contact ice unit k are located inside the waterline of the hull, or when the initial centroid of the contact ice unit k is located inside the waterline of the hull, the failure state is determined to be partial failure, and the shape of the contact ice unit k is changed. When more than a preset number M of the corner points of the contact ice unit k are located inside the waterline of the hull, the failure state is determined to be an overall failure, and the contact ice unit k is removed.

7. The method for calculating ship hull ice force according to claim 1, characterized in that, Dividing the ice floe area into several ice units includes: The ice floe area is divided into rectangular grids. While keeping the connection relationship between the corner points of the rectangular grid unchanged, the corner points of the rectangular grid are randomly moved within a preset range with their respective positions as the center, forming irregularly shaped ice units.

8. The method for calculating ship ice force according to claim 2, characterized in that, The hull waterline position information includes the position information of each discrete point, and the ice unit position information of any ship perimeter ice unit m includes the position information of each corner point of the ship perimeter ice unit m. Detecting the contact state between any ice element m around the ship and the waterline includes: Based on the position information of each corner point of the ship's perimeter ice unit m and the position information of the ship's waterline at the current moment, it is determined that at the current moment, the ship's perimeter ice unit m has at least one corner point located inside the ship's waterline and at least one corner point located outside the ship's waterline; or, based on the position information of the ship's waterline at the current moment, it is determined that at least one discrete point of the ship's waterline is located inside the ship's perimeter ice unit m, then it is determined that the ship's perimeter ice unit m is in contact with the ship's waterline.

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